File Organizations and Indexing
Lecture 5
R&G Chapter 8
"If you don't find it in the index, look very
carefully through the entire catalogue."
-- Sears, Roebuck, and Co.,
Consumer's Guide, 1897
Administrivia
• Homework 1 Assignment now Available
– Due in 2 parts: Sunday 9/14, Thursday 9/18
– Have to make changes to Postgres
– Don’t procrastinate
Review – The Big Picture
• Databases are cool
– Theory: data modelling, relational algebra
– Practical: storing data with disk, RAM
• Today:
– Practical: File Organization, Indexing
• Next Time:
– Theory: Relational Calculus
Review – Relational Algebra
• Basic operators for manipulating relations
–
–
–
–
–
–
Selection ( s )
Projection ( p )
Cross-product (  )
Set-difference ( — )
Union (  )
Rename ( ρ )
Selects a subset of rows
Retains only wanted columns
Combine two relations
Tuples in r1, but not in r2
Tuples in r1 and/or in r2
Change column name
• Other Useful Operators
– Intersection (  )
– Join (
)
– Division ( / )
Tuples in both relations
Match common columns
Tuples in A that match all in B
Relation Algebra 2: Division
• Division A / B,
– columns in A must be a superset of columns in B
– let Cboth be the columns in both A and B
– let CA-Only be the columns that are only in A
– result has columns CA-Only
– result has only rows where values in CA-Only have a
match with every value in B
– can be defined using other operators
Review: Examples of Division A/B
sno
s1
s1
s1
s1
s2
s2
s3
s4
s4
pno
p1
p2
p3
p4
p1
p2
p2
p2
p4
A
pno
p2
pno
p2
p4
B2
pno
p1
p2
p4
sno
s1
s2
s3
s4
sno
s1
s4
A/B1
A/B2
sno
s1
B1
B3
A/B3
sid bid
day
22 101 10/10/96
58 103 11/12/96
Reserves
Review:
Find the names of
Sailors who have
sid sname rating age
reserved all boats
Sailors
Boats
bid
101
102
103
104
bname
Interlake
Interlake
Clipper
Marine
22
31
58
dustin
lubber
rusty
color
Blue
Red
Green
Red
7
8
10
45.0
55.5
35.0
Find the names of sailors who’ve reserved all boats
• Uses division; schemas of the input relations to
/ must be carefully chosen:
 (Tempsids, (p
sid, bid
Re serves) / (p
bid
Boats))
p sname (Tempsids  Sailors)

To find sailors who’ve reserved all ‘Interlake’ boats:
.....
/p
bid
(s
bname ' Interlake'
Boats)
Review – Buffer Management and Files
• Storage of Data
– Fields, either fixed or variable length...
– Stored in Records...
– Stored in Pages...
– Stored in Files
• If data won’t fit in RAM, store on Disk
– Need Buffer Pool to hold pages in RAM
– Different strategies decide what to keep in pool
Today: File Organization
• How to keep pages of records on disk
• but must support operations:
– scan all records
– search for a record id “RID”
– search for record(s) with certain values
– insert new records
– delete old records
Alternative File Organizations
Many alternatives exist, tradeoffs for each:
– Heap files:
• Suitable when typical access is file scan of all records.
– Sorted Files:
• Best for retrieval in search key order
• Also good for search based on search key
–
Indexes: Organize records via trees or hashing.
•
•
Like sorted files, speed up searches for search key fields
Updates are much faster than in sorted files.
Indexes
• Sometimes need to retrieve records by the values in one
or more fields, e.g.,
– Find all students in the “CS” department
– Find all students with a gpa > 3
• An index on a file is a:
– Disk-based data structure
– Speeds up selections on the search key fields for the index.
– Any subset of the fields of a relation can be index search key
– Search key is not the same as key
• (e.g. doesn’t have to be unique ID).
• An index
– Contains a collection of data entries
– Supports efficient retrieval of all records with a given search
key value k.
First Question to Ask About Indexes
• What kinds of selections do they support?
– Selections of form field <op> constant
– Equality selections (op is =)
– Range selections (op is one of <, >, <=, >=, BETWEEN)
– More exotic selections:
• 2-dimensional ranges (“east of Berkeley and west of Truckee
and North of Fresno and South of Eureka”)
– Or n-dimensional
• 2-dimensional distances (“within 2 miles of Soda Hall”)
– Or n-dimensional
• Ranking queries (“10 restaurants closest to VLSB”)
• Regular expression matches, genome string matches, etc.
• One common n-dimensional index: R-tree
– Supported in Oracle and Informix
– See http://gist.cs.berkeley.edu for research on this topic
Index Classification
• What selections does it support
• Representation of data entries in index
– what info is the index storing? 3 alternatives:
• Data record with key value k
• <k, rid of data record with search key value k>
• <k, list of rids of data records with search key k>
• Clustered vs. Unclustered Indexes
• Single Key vs. Composite Indexes
• Tree-based, hash-based, other
Alternatives for Data Entry k* in Index
• Three alternatives:
 Actual data record (with key value k)
 <k, rid of matching data record>
 <k, list of rids of matching data records>
• Choice is orthogonal to the indexing technique.
– techniques: B+ trees, hash-tables, R trees, …
– Typically, index contains auxiliary information that
directs searches to the desired data entries
• Can have multiple (different) indexes per file.
– E.g. file sorted by age, with a hash index on salary
and a B+tree index on name.
Alternatives for Data Entries (Contd.)
• Alternative 1:
Actual data record (with key value k)
– Index structure is file organization for data records
(like Heap files or sorted files).
– At most one index on a table can use Alternative 1.
– Saves pointer lookups
– Can be expensive to maintain with insertions and
deletions.
Alternatives for Data Entries (Contd.)
Alternative 2
<k, rid of matching data record>
and Alternative 3
<k, list of rids of matching data records>
– Easier to maintain than Alt 1.
– At most one index can use Alternative 1; any others
must use Alternatives 2 or 3.
– Alternative 3 more compact than Alternative 2, but
leads to variable sized data entries even if search keys
are of fixed length.
– Even worse, for large rid lists the data entry might
have to span multiple pages!
Index Classification
• Clustered vs. unclustered:
– If order of data records is the same as, or `close to’,
order of index data entries, then called clustered index.
• A file can be clustered on at most one search key.
• Cost to retrieve data records with index varies
greatly based on whether index clustered or not!
• Alternative 1 implies clustered, but not vice-versa.
Clustered vs. Unclustered Index
• Suppose that Alternative (2) is used for data entries,
and that the data records are stored in a Heap file.
– To build clustered index, first sort the Heap file (with
some free space on each block for future inserts).
– Overflow blocks may be needed for inserts. (Thus, order of
data recs is `close to’, but not identical to, the sort order.)
CLUSTERED
Index entries
direct search for
data entries
Data entries
UNCLUSTERED
Data entries
(Index File)
(Data file)
Data Records
Data Records
Unclustered vs. Clustered Indexes
• What are the tradeoffs????
• Clustered Pros
– Efficient for range searches
– May be able to do some types of compression
– Possible locality benefits (related data?)
• Clustered Cons
– Expensive to maintain (on the fly or sloppy with
reorganization)
Hash-Based Indexes
• Good for equality selections.
• Index is a collection of buckets. Bucket = primary
page plus zero or more overflow pages.
• Hashing function h:
– h(r) = bucket in which record r belongs.
– h looks at the search key fields of r.
• If Alternative (1) is used, the buckets contain the
data records; otherwise, they contain <key, rid>
or <key, rid-list> pairs.
B+ Tree Indexes
Non-leaf
Pages
Leaf
Pages
Leaf pages contain data entries, and are chained (prev & next)
 Non-leaf pages contain index entries and direct searches:

index entry
P0
K 1
P1
K 2
P 2
K m Pm
Example B+ Tree
Root
17
Entries <= 17
5
2*
3*
Entries > 17
27
13
5*
7* 8*
14* 16*
22* 24*
30
27* 29*
33* 34* 38* 39*
• Find 28*? 29*? All > 15* and < 30*
• Insert/delete: Find data entry in leaf, then
change it. Need to adjust parent sometimes.
– And change sometimes bubbles up the tree
Comparing File Organizations
•
•
•
•
•
Heap files (random order; insert at eof)
Sorted files, sorted on <age, sal>
Clustered B+ tree file, Alternative (1), search
key <age, sal>
Heap file with unclustered B + tree index on
search key <age, sal>
Heap file with unclustered hash index on
search key <age, sal>
Operations to Compare
•
•
•
•
•
•
Scan: Fetch all records from disk
Fetch all records in sorted order
Equality search
Range selection
Insert a record
Delete a record
Cost Model for Analysis
I/O cost 150,000 times more than hash function
– We ignore CPU costs, for simplicity
B: The number of data pages
R: Number of records per page
F: Fanout of B-tree
Average-case analysis; based on several simplistic
assumptions.
 Good enough to show the overall trends!
Assumptions in Our Analysis
• Heap Files:
– Equality selection on key; exactly one match.
• Sorted Files:
– Files compacted after deletions.
• Indexes:
– Alt (2), (3): data entry size = 10% size of record
– Hash: No overflow buckets.
•
–
80% page occupancy => File size = 1.25 data size
Tree: 67% occupancy (this is typical).
•
Implies file size = 1.5 data size
I/O Cost of
Operations
Heap File
Scan all
records
Get all in
sort order
B: Number of data pages (packed)
R: Number of records per page
S: Time required for equality search
B
4B
Equality
Search
0.5 B
Range
Search
B
Insert
2
Delete
0.5B + 1
I/O Cost of
Operations
B: Number of data pages (packed)
R: Number of records per page
S: Time required for equality search
Sorted File
Scan all
records
B
Get all in
sort order
B
Equality
Search
log2 B
Range
Search
S + # matching
pages
Insert
S+B
Delete
S+B
I/O Cost of
Operations
B:
R:
F:
S:
Number of data pages (packed)
Number of records per page
Fanout of B-Tree
Time required for equality search
Clustered Tree
Scan all
records
1.5 B
Get all in
sort order
1.5 B
Equality
Search
logF (1.5 B)
Range
Search
S + #matching
pages
Insert
S+1
Delete
0.5B + 1
I/O Cost of
Operations
Unclustered Tree
Scan all
records
Get all in
sort order
B:
R:
F:
S:
Number of data pages (packed)
Number of records per page
Fanout of B-Tree
Time required for equality search
1.5 B
4B
Equality
Search
logF (1.5 B) + 1
Range
Search
S + #matching
records
Insert
S+2
Delete
S+2
I/O Cost of
Operations
Hash Index
Scan all
records
Get all in
sort order
B: Number of data pages (packed)
R: Number of records per page
S: Time required for equality search
1.25 B
4B
Equality
Search
2
Range
Search
1.25 B
Insert
4
Delete
S+2
B:
R:
F:
S:
I/O Cost of
Operations
The number of data pages
Number of records per page
Fanout of B-Tree
Time required for equality search
Heap File
Sorted File
Clustered Tree
Unclustered Tree
Hash Index
Scan all
records
B
B
1.5 B
1.5 B
1.25 B
Get all in
sort
order
4B
B
1.5 B
4B
4B
Equality
Search
0.5 B
log2 B
logF (1.5 B)
logF (1.5 B)
+1
2
Range
Search
B
S+
S+
#matching #matching
pages
pages
S+
#matching
records
1.25 B
Insert
2
S+B
S+1
S+2
4
Delete
0.5B + 1
S+B
0.5B + 1
S+2
S+2
Index Selection Guidelines
• Attributes in WHERE clause are candidates for index keys.
– Exact match condition suggests hash index.
– Range query suggests tree index.
• Clustering is especially useful for range queries; can also help on
equality queries if there are many duplicates.
• Multi-attribute search keys should be considered when a WHERE
clause contains several conditions.
– Order of attributes is important for range queries.
– Such indexes sometimes enable index-only strategies
•
For index-only strategies, clustering is not important!
• Choose indexes that benefit as many queries as possible.
• Since only one index can be clustered per table, choose it based
on important queries that would benefit the most from
clustering.
Examples of Clustered Indexes
• B+ tree index on E.age can be
used to get qualifying tuples.
– How selective is the condition?
– Is the index clustered?
• Consider the GROUP BY query.
– If many tuples have E.age > 10,
using E.age index and sorting the
retrieved tuples may be costly.
– Clustered E.dno index may be
better!
• Equality queries and duplicates:
– Clustering on E.hobby helps!
SELECT E.dno
FROM Emp E
WHERE E.age>40
SELECT E.dno, COUNT (*)
FROM Emp E
WHERE E.age>10
GROUP BY E.dno
SELECT E.dno
FROM Emp E
WHERE E.hobby=Stamps
Indexes with Composite Search Keys
• Composite Search Keys: Search
on a combination of fields.
– Equality query: Every field value is
equal to a constant value. E.g. wrt
<sal,age> index:
• age=20 and sal =75
–
Range query: Some field value is
not a constant. E.g.:
• age =20; or age=20 and sal > 10
• Data entries in index sorted by
search key to support range
queries.
– Lexicographic order, or
– Spatial order.
Examples of composite key
indexes using lexicographic order.
11,80
11
12,10
12
12,20
13,75
<age, sal>
10,12
20,12
75,13
name age sal
bob 12
10
cal 11
80
joe 12
20
sue 13
75
12
13
<age>
10
Data records
sorted by name
80,11
<sal, age>
Data entries in index
sorted by <sal,age>
20
75
80
<sal>
Data entries
sorted by <sal>
Composite Search Keys
• To retrieve Emp records with age=30 AND sal=4000,
an index on <age,sal> would be better than an index
on age or an index on sal.
– Choice of index key orthogonal to clustering etc.
• If condition is: 20<age<30 AND 3000<sal<5000:
– Clustered tree index on <age,sal> or <sal,age> is best.
• If condition is: age=30 AND 3000<sal<5000:
– Clustered <age,sal> index much better than <sal,age>
index!
• Composite indexes are larger, updated more often.
Index-Only Plans
<E.dno>
SELECT D.mgr
FROM Dept D, Emp E
WHERE D.dno=E.dno
• A number of queries <E.dno,E.eid> SELECT D.mgr, E.eid
FROM Dept D, Emp E
can be answered
Tree index!
WHERE D.dno=E.dno
without retrieving
any tuples from one
SELECT E.dno, COUNT(*)
<E.dno> FROM Emp E
or more of the
relations involved if
GROUP BY E.dno
a suitable index is
SELECT E.dno, MIN(E.sal)
<E.dno,E.sal> FROM Emp E
available.
Tree index! GROUP BY E.dno
<E. age,E.sal> SELECT AVG(E.sal)
or
FROM Emp E
<E.sal, E.age> WHERE E.age=25 AND
Tree! E.sal BETWEEN 3000 AND 5000
Index-Only Plans (Contd.)
• Index-only plans
are possible if the
key is <dno,age>
or we have a tree
index with key
<age,dno>
– Which is better?
– What if we
consider the
second query?
SELECT E.dno, COUNT (*)
FROM Emp E
WHERE E.age=30
GROUP BY E.dno
SELECT E.dno, COUNT (*)
FROM Emp E
WHERE E.age>30
GROUP BY E.dno
Summary
• Alternative file organizations, tradeoffs for each
• If selection queries are frequent, sorting the file
or building an index is important.
– Hash-based indexes only good for equality search.
– Sorted files and tree-based indexes best for range
search; also good for equality search. (Files rarely
kept sorted in practice; B+ tree index is better.)
• Index is a collection of data entries plus a way to
quickly find entries with given key values.
Summary (Contd.)
• Data entries can be actual data records, <key,
rid> pairs, or <key, rid-list> pairs.
– Choice orthogonal to indexing technique used to
locate data entries with a given key value.
• Can have several indexes on a given file of data
records, each with a different search key.
• Indexes can be
– clustered, unclustered
– B-tree, hash table, etc.
Summary (Contd.)
• Understanding the nature of the workload for the
application, and the performance goals, is essential
to developing a good design.
– What are the important queries and updates? What
attributes/relations are involved?
• Indexes must be chosen to speed up important
queries (and perhaps some updates!).
– Index maintenance overhead on updates to key fields.
– Choose indexes that can help many queries, if possible.
– Build indexes to support index-only strategies.
– Clustering is an important decision; only one index on a
given relation can be clustered!
– Order of fields in composite index key can be important.